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Chapter 20: Problem 41

A \(1 M\) solution of \(\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}\) is placed in a beaker with a strip of Cu metal. A \(1 M\) solution of \(\mathrm{SnSO}_{4}\) is placed in a second beaker with a strip of Sn metal. A salt bridge connects the two beakers, and wires to a voltmeter link the two metal electrodes. (a) Which electrode serves as the anode and which as the cathode? (b) Which electrode gains mass and which loses mass as the cell reaction proceeds? (c) Write the equation for the overall cell reaction. (d) What is the emf generated by the cell under standard conditions?

Short Answer

Expert verified
\( (a) \) Anode: Sn electrode; Cathode: Cu electrode \( (b) \) Electrode that gains mass: Cu electrode (cathode); Electrode that loses mass: Sn electrode (anode) \( (c) \) Overall cell reaction: \(\mathrm{Sn(s) + Cu^{2+}(aq) \rightarrow Sn^{2+}(aq) + Cu(s)}\) \( (d) \) The emf generated by the cell under standard conditions is 0.48 V.

Step by step solution

01

Consult the standard reduction potential table

We will consult the standard reduction potential table to determine the reduction potentials for Cu(II) and Sn(II). \[\mathrm{Cu^{2+}(aq) + 2e^{-} \rightarrow Cu(s)}\hspace{10mm} E^\circ_{\mathrm{Cu^{2+}/Cu}} = +0.34\,\mathrm{V}\] \[\mathrm{Sn^{2+}(aq) + 2e^{-} \rightarrow Sn(s)}\hspace{10mm} E^\circ_{\mathrm{Sn^{2+}/Sn}} = -0.14\,\mathrm{V}\]
02

Identify the anode and cathode

In a galvanic cell, the electrode with the more positive reduction potential is the cathode, where reduction occurs. The electrode with the more negative reduction potential is the anode, where oxidation occurs. In this case, since the Cu(II) reduction potential is more positive than the Sn(II) reduction potential, Cu(II) will be the cathode and Sn(II) will be the anode. (a) Anode: Sn electrode; Cathode: Cu electrode
03

Determine mass gain and mass loss in electrodes

At the anode, oxidation occurs, leading to a loss of mass as the metal dissolves and goes into the solution. In contrast, at the cathode, reduction occurs, and the metal ion gains electrons to form solid metal atoms, which deposit on the electrode causing an increase in mass. (b) Electrode that gains mass: Cu electrode (cathode); Electrode that loses mass: Sn electrode (anode)
04

Write the overall cell reaction

First, write the half-reactions: Oxidation (anode): \[\mathrm{Sn(s) \rightarrow Sn^{2+}(aq) + 2e^{-}}\] Reduction (cathode): \[\mathrm{Cu^{2+}(aq) + 2e^{-} \rightarrow Cu(s)}\] Now, add the half-reactions to obtain the overall cell reaction: \[\mathrm{Sn(s) + Cu^{2+}(aq) \rightarrow Sn^{2+}(aq) + Cu(s)}\] (c) Overall cell reaction: \[\mathrm{Sn(s) + Cu^{2+}(aq) \rightarrow Sn^{2+}(aq) + Cu(s)}\]
05

Calculate the cell potential under standard conditions

We can calculate the emf (cell potential) generated by the cell under standard conditions using the Nernst equation: \[E_\mathrm{cell}^\circ = E_\mathrm{cathode}^\circ - E_\mathrm{anode}^\circ\] Substitute the values: \[E_\mathrm{cell}^\circ = (+0.34\,\mathrm{V}) - (-0.14\,\mathrm{V})\] \[E_\mathrm{cell}^\circ = +0.48\, \mathrm{V}\] (d) The emf generated by the cell under standard conditions is 0.48 V.

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Most popular questions from this chapter

Indicate whether the following balanced equations involve oxidation-reduction. If they do, identify the elements that undergo changes in oxidation number. $$ \begin{array}{l} \text { (a) } \mathrm{PBr}_{3}(l)+3 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{3} \mathrm{PO}_{3}(a q)+3 \mathrm{HBr}(a q) \\ \text { (b) } \mathrm{NaI}(a q)+3 \mathrm{HOCl}(a q) \longrightarrow \mathrm{NaIO}_{3}(a q)+3 \mathrm{HCl}(a q) \\ \text { (c) } 3 \mathrm{SO}_{2}(g)+2 \mathrm{HNO}_{3}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\ 3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NO}(g) \\ \text { (d) } 2 \mathrm{H}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{NaBr}(s) \longrightarrow \\ \mathrm{Br}_{2}(l)+\mathrm{SO}_{2}(g)+\mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \end{array} $$

During a period of discharge of a lead-acid battery, \(402 \mathrm{~g}\) of \(\mathrm{Pb}\) from the anode is converted into \(\mathrm{PbSO}_{4}(s) .\) (a) What mass of \(\mathrm{PbO}_{2}(s)\) is reduced at the cathode during this same period? (b) How many coulombs of electrical charge are transferred from \(\mathrm{Pb}\) to \(\mathrm{PbO}_{2} ?\)

In a galvanic cell the cathode is an \(\mathrm{Ag}^{+}(1.00 \mathrm{M}) / \mathrm{Ag}(s)\) halfcell. The anode is a standard hydrogen electrode immersed in a buffer solution containing \(0.10 \mathrm{M}\) benzoic acid \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COOH}\right)\) and \(0.050 \mathrm{M}\) sodium benzoate \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{COO}^{-} \mathrm{Na}^{+}\right) .\) The measured cell voltage is \(1.030 \mathrm{~V}\). What is the \(\mathrm{p} K_{a}\) of benzoic acid?

The Haber process is the principal industrial route for converting nitrogen into ammonia: $$\mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g)$$ (a) What is being oxidized, and what is being reduced? (b) Using the thermodynamic data in Appendix \(\mathrm{C}\), calculate the equilibrium constant for the process at room temperature. (c) Calculate the standard emf of the Haber process at room temperature.

A common shorthand way to represent a voltaic cell is anode|anode solution \(\|\) cathode solution \(\mid\) cathode A double vertical line represents a salt bridge or a porous barrier. A single vertical line represents a change in phase, such as from solid to solution. (a) Write the half-reactions and overall cell reaction represented by \(\mathrm{Fe}\left|\mathrm{Fe}^{2+} \| \mathrm{Ag}^{+}\right| \mathrm{Ag} ;\) sketch the cell. (b) Write the half-reactions and overall cell reaction represented by \(\mathrm{Zn}\left|\mathrm{Zn}^{2+} \| \mathrm{H}^{+}\right| \mathrm{H}_{2}\); sketch the cell. (c) Using the notation just described, represent a cell based on the following reaction: $$ \begin{aligned} \mathrm{ClO}_{3}^{-}(a q)+3 \mathrm{Cu}(s)+6 \mathrm{H}^{+}(a q) & \mathrm{Cl}^{-}(a q)+3 \mathrm{Cu}^{2+}(a q)+3 \mathrm{H}_{2} \mathrm{O}(l) \end{aligned} $$ \(\mathrm{Pt}\) is used as an inert electrode in contact with the \(\mathrm{ClO}_{3}^{-}\) and \(\mathrm{Cl}^{-}\). Sketch the cell.
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